# slarra (l) - Linux Man Pages

## NAME

SLARRA - the splitting points with threshold SPLTOL

## SYNOPSIS

SUBROUTINE SLARRA(
N, D, E, E2, SPLTOL, TNRM, NSPLIT, ISPLIT, INFO )

IMPLICIT NONE

INTEGER INFO, N, NSPLIT

REAL SPLTOL, TNRM

INTEGER ISPLIT( * )

REAL D( * ), E( * ), E2( * )

## PURPOSE

Compute the splitting points with threshold SPLTOL. SLARRA sets any "small" off-diagonal elements to zero.

## ARGUMENTS

N (input) INTEGER
The order of the matrix. N > 0.
D (input) REAL array, dimension (N)
On entry, the N diagonal elements of the tridiagonal matrix T.
E (input/output) REAL array, dimension (N)
On entry, the first (N-1) entries contain the subdiagonal elements of the tridiagonal matrix T; E(N) need not be set. On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT, are set to zero, the other entries of E are untouched.
E2 (input/output) REAL array, dimension (N)
On entry, the first (N-1) entries contain the SQUARES of the subdiagonal elements of the tridiagonal matrix T; E2(N) need not be set. On exit, the entries E2( ISPLIT( I ) ), 1 <= I <= NSPLIT, have been set to zero SPLTOL (input) REAL The threshold for splitting. Two criteria can be used:
SPLTOL<0 : criterion based on absolute off-diagonal value
SPLTOL>0 : criterion that preserves relative accuracy TNRM (input) REAL The norm of the matrix.
NSPLIT (output) INTEGER
The number of blocks T splits into. 1 <= NSPLIT <= N.
ISPLIT (output) INTEGER array, dimension (N)
The splitting points, at which T breaks up into blocks. The first block consists of rows/columns 1 to ISPLIT(1), the second of rows/columns ISPLIT(1)+1 through ISPLIT(2), etc., and the NSPLIT-th consists of rows/columns ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
INFO (output) INTEGER
= 0: successful exit

## FURTHER DETAILS

Based on contributions by

Beresford Parlett, University of California, Berkeley, USA
Jim Demmel, University of California, Berkeley, USA

Inderjit Dhillon, University of Texas, Austin, USA

Osni Marques, LBNL/NERSC, USA

Christof Voemel, University of California, Berkeley, USA